Problem 5. Let f(n) be a function of positive integer n. We know: f(1)f(n)=1=f(n/4)+f(n/2)+n. Prove f(n)=O(n). Problem 6. Consider a set S of n integers that are stored in an array (not necessarily sorted). Let e and e be two integers in S such that e is positioned before e. We call the pair (e,e) an inversion in S if e>e. Write an algorithm to report all the inversions in S. Your algorithm must terminate in O(n2) time. For example, if the array stores the sequence (10,15,7,12), then your algorithm should return (10,7),(15,7), and (15,12)